Calculus Examples

$\frac{\sqrt{2}}{2} - \frac{π}{4} \cdot \frac{\sqrt{2}}{2}$

Step 1

Multiply $- \frac{π}{4} \cdot \frac{\sqrt{2}}{2}$ .

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Step 1.1

Multiply $\frac{\sqrt{2}}{2}$ by $\frac{π}{4}$ .

$\frac{\sqrt{2}}{2} - \frac{\sqrt{2} π}{2 \cdot 4}$

Step 1.2

Multiply $2$ by $4$ .

$\frac{\sqrt{2}}{2} - \frac{\sqrt{2} π}{8}$

Step 2

To write $\frac{\sqrt{2}}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\sqrt{2}}{2} \cdot \frac{4}{4} - \frac{\sqrt{2} π}{8}$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{\sqrt{2}}{2}$ by $\frac{4}{4}$ .

$\frac{\sqrt{2} \cdot 4}{2 \cdot 4} - \frac{\sqrt{2} π}{8}$

Step 3.2

Multiply $2$ by $4$ .

$\frac{\sqrt{2} \cdot 4}{8} - \frac{\sqrt{2} π}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{\sqrt{2} \cdot 4 - \sqrt{2} π}{8}$

Step 5

Move $4$ to the left of $\sqrt{2}$ .

$\frac{4 \sqrt{2} - \sqrt{2} π}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{4 \sqrt{2} - \sqrt{2} π}{8}$

Decimal Form:

$0.15174641 \dots$